Principle of Random Wave-Function Phase of the Final State in Free-Electron Emission in a Wiggler

The typical values of R = quantum energy/potential amplitude in electron energy of an incident radiation treated in quantum electrodynamics, an electric wiggler, and a magnetic wiggler are 108, 10–4 and 10–10, respectively. Therefore, the interaction of a free electron with these fields cannot be described with the same principle. The wave-function phase of the final state through a transition route in a wiggler emission is unrelated to that through any other route, while that in photon scattering treated in quantum electrodynamics is routeindependent. From this, we can explain the reason why the power of free-electron twoquantum Stark (FETQS) emission driven by macroscopic motion in an electric wiggler scales as 1/ 2, contradicting the correspondence principle, and is many powers of ten (e.g., 1019) times stronger than the value calculated with the quantum electrodynamic concept.